This invention is in the field of digital communications and relates to a digital modulation method referred to as Quadrature Amplitude Modulation (QAM). QAM modems can be configured to provide very spectrally efficient transmission and are thus often used in systems where high speed data communications are required over band-limited channels. There are many types of such systems, including fixed point-to-point radio communication links, mobile radio communication links, satellite communication links, and cable communication links.
A QAM signal can be created by amplitude modulating, with user data bits, two RF carriers shifted in phase by 90°, i.e., carriers in quadrature, then combining these carriers to form a composite carrier. When a sequence of 2n data bits, where n is an integer, modulates a QAM modulator, the amplitude vector of the combined carrier signal terminates on one of 22n positions. The 22n positions when graphically represented on a phase plane diagram create what is commonly referred to as a signal point constellation. The commonly applied 22n constellations are square shaped and Gray coded. With Gray coding the digital sequence represented by each signal point in the constellation differs from the digital sequence represented by any immediately adjacent signal point in only one bit position. As a result, any signal point which suffers corruption during transmission and is decoded mistakenly as an adjacent signal point contains only a single bit error.
A problem with a square array of 22n signal points, where n>1, is that the points at the corners of the square have relatively large amplitudes compared to the average amplitude, and hence result in a high peak-to-average power ratio (PAPR) at the modulator output. QAM requires linear amplification if the signal constellation as created is to be preserved. Because of the high PAPR of a square 22n signal point constellation where n>1, the amplifier following the modulator must be operated at an average power level that is lower, by at least the PAPR, than the amplifier's saturation level, i.e., the level at which the amplifier's performance is no longer linear. For a given value of n, where n>1, a non-square 22n signal point constellation, if its PAPR is lower than that of the 22n square signal point constellation, results in a higher achievable average transmitted power level than that achievable with the square signal point constellation. Such a non-square constellation is thus desirable in several system types if it does not deteriorate the receiver's bit-error-rate (BER) versus the ratio of received signal to received noise in bit rate bandwidth (S/Nb) performance such that the receiver sensitivity, i.e., the receiver input signal level required for a specified BER, is increased relative to that of the square constellation by as much or more than the increase in the average transmitted power afforded by the non-squared constellation.
In the case of most single carrier systems, a non-square constellation with the above outlined properties is clearly advantageous. In the case of multi-carrier systems, the multicarrier signal PAPR may or may not be strongly correlated with that of the individual sub-carriers PAPR. For example, in OFDMA, the correlation is poor. However, with Discrete Fourier Transform-Spread OFDM (DFT-Spread OFDM), any reduction in the PAPR of the individual sub-carriers results in a reduction of the multicarrier signal PAPR. Further, if the DFT-Spread OFDM sub-carrier mapping is Interleaved FDMA (IFDMA), then the PAPR of the multicarrier signal is reduced to the same value as that of the individual subcarriers, this reduction being the maximum achievable. Thus, for systems employing DFT-Spread OFDM and QAM modulated subcarriers, sub-carriers with non-square 22n signal point constellations having PAPRs lower than those of square 22n point constellations would be highly desirable, provided that any deterioration in the receiver sensitivity is measurably less than the accompanying decrease in PAPR.